A flow in which a thin film falls due to gravity on the inner surface of a vertical, rotating cylinder is investigated. This is performed using two-dimensional (2D) and 3D direct numerical simulations, with a volume-of-fluid approach to treat the interface. The problem is parameterized by the Reynolds, Froude, Weber, and Ekman numbers. The variation of the Ekman number (Ek), defined to be proportional to the rotational speed of the cylinder, has a strong effect on the flow characteristics. Simulations are conducted over a wide range of Ek values ($0\le \text{Ek}\le 484$) in order to provide detailed insight into how this parameter influences the flow. Our results indicate that increasing Ek, which leads to a rise in the magnitude of centrifugal forces, produces a stabilizing effect, suppressing wave formation. Key flow features, such as the transition from a 2D to a more complex 3D wave regime, are influenced significantly by this stabilization and are investigated in detail. Furthermore, the imposed rotation results in distinct flow characteristics such as the development of angled waves, which arise due to the combination of gravitationally and centrifugally driven motion in the axial and azimuthal directions, respectively. We also use a weighted residuals integral boundary layer method to determine a boundary in the space of Reynolds and Ekman numbers that represents a threshold beyond which waves have recirculation regions.

Charged-particle dynamics in a strong constant magnetic field can yield a fast gyromotion with high frequency around the center. Considering the superior of exponential integrators for highly oscillatory problems and the benefit of energy preservation of numerical integrators in solving the charged-particle dynamics, this paper is devoted to developing a fourth-order energy-preserving exponential integrator for the charged-particle dynamics in a strong constant magnetic field. To this end, we first rewrite the problem in the form of a semilinear Poisson system, to which the exponential average vector field (EAVF) method can be applied with energy preservation. Then, by deriving the truncated modified differential equation of the EAVF method, we propose a fourth-order energy-preserving exponential integrator according to the modifying integrator theory. Finally, numerical results soundly support the good energy preservation and high efficiency of the proposed fourth-order integrator in solving the problem considered in this paper.

Numerically reproducing the process of thrombus formation is highly desired for understanding its mechanism but still remains challenging due to the polydisperse feature of blood components and their multiple biochemical or biomechanical behaviors involved. We numerically implemented a simplified version of the process from the perspective of biomechanics, using a mesoscale particle-based method, smoothed dissipative particle dynamics-immersed boundary method. This version covers the adhesion and aggregation of platelets (PLTs), the deformation and aggregation of red blood cells (RBCs), and the interaction between PLTs and RBCs, as well as the blockage of microvessels. Four critical factors that can affect thrombus formation were investigated: the velocity of blood flow, the adhesive ability of PLTs, the interaction strength between PLTs and RBCs, and the deformability of RBCs. Increasing the velocity of blood flow was found to be the most effective way to reduce the microvessel blockage, and reducing the adhesive ability of PLTs is also a direct and efficient way. However, decreasing the interaction strength between PLTs and RBCs sometimes does not alleviate thrombus formation, and similarly, increasing the deformability of RBCs does not have a significant improvement for the severely blocked microvessel. These results imply that maintaining high-rate blood flow plays a crucial role in the prevention and treatment of thrombosis, which is even more effective than antiplatelet or anticoagulant drugs. The drugs or treatments concentrating on reducing the PLT-RBC interaction or softening the RBCs may not have a significant effect on the thrombosis.

Effect of concurrent alignment and repulsion is studied in the purview of a confined active matter system using a modified force-based Vicsek model. On alteration of the alignment and the repulsive force parameters, a low alignment random phase, a midrange alignment milling phase, and a high alignment oscillatory phase are identified. Based on the particle aggregations, the milling phase is further classified into three subphases, two of which are spatial patterns: one consisting of compact ring-shaped mills and the other incorporating both rings and clusters. A correlation function based on the inner product of spatial velocity fluctuations of the particles shows a high correlation length for the ringed milling and the rings-clusters hybrid milling state. On analyzing temporal velocity fluctuations of particles through chaos detection techniques, low alignment and high alignment states are indicative of chaos, while the middle order alignment is symbolic of periodicity. The extent of synchronization of the particles' motion is analyzed through a Hilbert transform-based mean frequency approach, leading to the detection of a weak chimera state in the case of the spatial structures. The ringed milling state shows a unique category of weak chimera consisting of multiple oscillator groups showcasing different synchronization frequencies coexisting with desynchronized oscillators.

We have studied a class of marginally jammed states in a system of hard disks confined in a narrow channel—a quasi-one-dimensional system—whose exponents are not those predicted by theories valid in the infinite dimensional limit. The exponent $\gamma$ which describes the distribution of small gaps takes the value 1 rather than the infinite dimensional value $0.41269\cdots$. Our work shows that there exist jammed states not found within the tiling approach of Ashwin and Bowles. The most dense of these marginal states is an unusual state of matter that is asymptotically crystalline.

We perform three-dimensional particle-based simulations of confined, vibrated, and magnetizable beads to study the effect of cell geometry on pattern selection. For quasi-two-dimensional systems, we reproduce previously observed macroscopic patterns such as hexagonal crystals and labyrinthine structures. For systems at the crossover from two to three dimensions, labyrinthine branches shorten and are replaced by triplets of beads forming upright triangles which self-organize into a herringbone pattern. This transition is associated with increases in both translational and orientational orders.

We have used video imaging and interferometric techniques to investigate the dynamics of spreading of drops of ${}^4\mathrm{He}$ on a solid surface for temperatures ranging from 5.2 K (near the critical point) to 2.2 K (near $T_{\lambda }$). After an initial transient, the drops become pancake-shaped with a radius that grows as $R\left(t\right)\approx t^{\alpha },$ with $\alpha =0.149\pm 0.002$. The drops eventually begin to shrink due to evaporation driven by gravitational and curvature effects, which limits their lifetime to about 1000 s. Although helium completely wets the substrate, and the spreading takes place over a pre-existing adsorbed film, a distinct contact line with a contact angle of order one degree is visible throughout this process.

In contrast to normal diffusion, there is no canonical model for reactions between chemical species which move by anomalous subdiffusion. Indeed, the type of mesoscopic equation describing reaction-subdiffusion systems depends on subtle assumptions about the microscopic behavior of individual molecules. Furthermore, the correspondence between mesoscopic and microscopic models is not well understood. In this paper, we study the subdiffusion-limited model, which is defined by mesoscopic equations with fractional derivatives applied to both the movement and the reaction terms. Assuming that the reaction terms are affine functions, we show that the solution to the fractional system is the expectation of a random time change of the solution to the corresponding integer order system. This result yields a simple and explicit algebraic relationship between the fractional and integer order solutions in Laplace space. We then find the microscopic Langevin description of individual molecules that corresponds to such mesoscopic equations and give a computer simulation method to generate their stochastic trajectories. This analysis identifies some precise microscopic conditions that dictate when this type of mesoscopic model is or is not appropriate. We apply our results to several scenarios in cell biology which, despite the ubiquity of subdiffusion in cellular environments, have been modeled almost exclusively by normal diffusion. Specifically, we consider subdiffusive models of morphogen gradient formation, fluctuating mobility, and fluorescence recovery after photobleaching (FRAP) experiments. We also apply our results to fractional ordinary differential equations.

We experimentally study the complex dynamics of two mutually coupled physically dissimilar oscillators with two different kinds of coupling mechanisms. Specifically, an optoelectronic oscillator is coupled to a Colpitts oscillator via optical power and the Colpitts oscillator is coupled back to the optoelectronic oscillator via electric voltage. We investigate and characterize phase synchronization and generalized chaos synchronization in this coupled system. Phase synchronization is observed when both oscillators are preset to oscillate periodically prior to coupling while generalized chaos synchronization is observed when both oscillators are preset to oscillate chaotically prior to coupling. In the periodical oscillation regime, we observe a linear relationship between the strengths of the two unidirectional coupling factors at which the system transitions to a synchronized state. In the chaotic regime, we observe a transition from hyperchaos to chaos associated with the onset of generalized synchronization.

We analyze the late-time relaxation dynamics for a general contagion model. In this model, nodes are either active or failed. Active nodes can fail either “spontaneously” at any time or “externally” if their neighborhoods are sufficiently damaged. Failed nodes may always recover spontaneously. At late times, the breaking of time-translation invariance is a necessary condition for physical aging. We observe that time-translational invariance is lost for initial conditions that lie between the basins of attraction of the model's two stable stationary states. Based on corresponding mean-field predictions, we characterize the observed model behavior in terms of a phase diagram spanned by the fractions of spontaneously and externally failed nodes. For the square lattice, the phases in which the dynamics approaches one of the two stable stationary states are not linearly separable due to spatial correlation effects. Our results provide insights into aging and relaxation phenomena that are observable in a model of social contagion processes.

We present a Monte Carlo study of the effects of elastic anisotropy on the topological defects which can be formed in nematic films with hybrid boundary conditions. We simulate the polarized microscopy images and analyze their evolution in uniaxial systems for different values of the Frank elastic constants.

We study the dynamics of an intruder moving through a fluidized granular medium in three dimensions ($d=3$). The intruder and grains have both translational and rotational degrees of freedom. The energy-dissipation mechanism is solid friction between all pairs of particles. We keep the granular system fluidized even at rather high densities by randomly perturbing the linear and angular velocities of the grains. We apply a constant external force of magnitude $F$ to the intruder and obtain its steady-state velocity $V_s$ in the center-of-mass frame of the grains. The $F-V_s$ relation is of great interest in the industrial processing of granular matter and has been the subject of most experiments on this problem. We also obtain the mobility, which is proportional to the inverse viscosity, as a function of the volume fraction $\varphi$. This is shown to diverge at the jamming volume fraction. For $\varphi$ below the jamming fraction, we find that $V_s\sim F$ for small $F$ and $V_s\sim F^{1/2}$ for large $F$. The intruder shows diffusive motion in the plane perpendicular to the direction of the external force.

We consider the quality factor $\mathcal{Q}$, which quantifies the trade-off between power, efficiency, and fluctuations in steady-state heat engines modeled by dynamical systems. We show that the nonlinear scattering theory, in both classical and quantum mechanics, sets the bound $\mathcal{Q}=3/8$ when approaching the Carnot efficiency. On the other hand, interacting, nonintegrable, and momentum-conserving systems can achieve the value $\mathcal{Q}=1/2$, which is the universal upper bound in linear response. This result shows that interactions are necessary to achieve the optimal performance of a steady-state heat engine.

We used a thermodynamic integration scheme, which is specifically designed for disordered systems, to compute the interfacial free energy of the solid-liquid interface in the hard-sphere model. We separated the bulk contribution to the total free energy from the interface contribution, performed a finite-size scaling analysis, and obtained for the (100)-interface $\gamma =0.591\left(11\right)k_{\mathrm{B}}T{\sigma }^{-2}$.

We show that a Parrondo paradox can emerge in two-state quantum walks without resorting to experimentally intricate high-dimensional coins. To achieve such goal we employ a time-dependent coin operator without breaking the translation spatial invariance of the system.

We consider the optimization problem of seeding a spreading process on a temporal network so that the expected size of the resulting outbreak is maximized. We frame the problem for a spreading process following the rules of the susceptible-infected-recovered model with temporal scale equal to the one characterizing the evolution of the network topology. We perform a systematic analysis based on a corpus of 12 real-world temporal networks and quantify the performance of solutions to the influence maximization problem obtained using different level of information about network topology and dynamics. We find that having perfect knowledge of the network topology but in a static and/or aggregated form is not helpful in solving the influence maximization problem effectively. Knowledge, even if partial, of the early stages of the network dynamics appears instead essential for the identification of quasioptimal sets of influential spreaders.

Epigenetic modifications of histones crucially affect eukaryotic gene activity, while the epigenetic histone state is largely determined by the binding of specific factors such as the transcription factors (TFs) to DNA. Here, the way in which the TFs and the histone state are dynamically correlated is not obvious when the TF synthesis is regulated by the histone state. This type of feedback regulatory relation is ubiquitous in gene networks to determine cell fate in differentiation and other cell transformations. To gain insights into such dynamical feedback regulations, we theoretically analyze a model of epigenetic gene switching by extending the Doi-Peliti operator formalism of reaction kinetics to the problem of coupled molecular processes. Spin-1 and spin-1/2 coherent-state representations are introduced to describe stochastic reactions of histones and binding or unbinding of TFs in a unified way, which provides a concise view of the effects of timescale difference among these molecular processes; even in the case that binding or unbinding of TFs to or from DNA is adiabatically fast, the slow nonadiabatic histone dynamics gives rise to a distinct circular flow of the probability flux around basins in the landscape of the gene state distribution, which leads to hysteresis in gene switching. In contrast to the general belief that the change in the amount of TF precedes the histone state change, flux drives histones to be modified prior to the change in the amount of TF in self-regulating circuits. Flux-landscape analyses shed light on the nonlinear nonadiabatic mechanism of epigenetic cell fate decision making.

As a cooperative act decreases an individual's fitness for others to benefit, it is expected to be selected against by natural selection. That, how contrary to this naive expectation cooperation has evolved, is a fundamental problem in evolutionary biology and social sciences. Here, by introducing a mathematical model, we show that coevolution of cooperation and language can provide an avenue through which both cooperation and language evolve. In this model, individuals in a population play a prisoner's dilemma game and at the same time try to communicate a set of representations by producing signals. For this purpose, individuals try to build a common language, which is composed of a set of signal-representation associations. Individuals decide in language learning based on their payoff from the prisoner's dilemma game and decide about their strategy in the prisoner's dilemma game based on their success in conveying symbolic information. The model shows cooperators are able to build a common language and protect it against defectors' attempt to decode it. The language channels the benefit of cooperation toward cooperators, and defectors, being banished from the language, are unable to exploit cooperators, and are doomed to extinction.

Living matter often exhibits multimode transport that switches between an active, self-propelled motion and a seemingly passive, random motion. Here, we investigate an exactly solvable model of multimode active matter, such as living cells and motor proteins, which alternatingly undergoes active and passive motion. Our model study shows that the reversible transition between a passive mode and an active mode causes super-Gaussian transport dynamics, observed in various experiments. We find the non-Gaussian character of the matter's displacement distribution is essentially determined by the population ratio between active and passive motion. Interestingly, under a certain population ratio of the active and passive modes, the displacement distribution changes from sub-Gaussian to super-Gaussian as time increases. The mean-square displacement of our model exhibits transient superdiffusive dynamics, yet recovers diffusive behavior at both the short- and long-time limits. We finally generalize our model to encompass complex, multimode active matter in an arbitrary spatial dimension.